The epidemic of COVID-19 reached different areas of China at different times. This means that different locations were at different phases of their own outbreaks at the time of the Wuhan lockdown (23 January) and other provincial and national actions taken with the intent of minimizing transmission. Data from the ensuing epidemics in China may be informative to other countries that are considering taking action.
Here we look at the final size of the outbreak in each province as a function of the date that the first case was reported. Next we look at the final size of the outbreak in each province as a function of the size of the outbreak on 23 January.
These results illustrate the importance of taking early actions to mitigate transmission prior to confirmation of a large number of local cases. Importantly, at the time of the Wuhan lockdown, no province other than Hubei was reporting more than 40 cases. These results also support a calculation of the costs of delaying intervention. A linear regression quantifies the effect of delay on outbreak size. The correlation between outbreak size and days elapsed is about 0.9.
##
## Call:
## lm(formula = log10(outbreak.size) ~ cases$Date[outbreak.start])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49104 -0.26188 0.00321 0.22222 0.65866
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4823.64030 448.01992 10.77 1.20e-11 ***
## cases$Date[outbreak.start] -0.26370 0.02451 -10.76 1.22e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3496 on 29 degrees of freedom
## Multiple R-squared: 0.7997, Adjusted R-squared: 0.7928
## F-statistic: 115.8 on 1 and 29 DF, p-value: 1.218e-11
##
## Pearson's product-moment correlation
##
## data: as.numeric(log10(outbreak.size)) and as.numeric(cases$Date[outbreak.start])
## t = -10.761, df = 29, p-value = 1.218e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.9481629 -0.7903905
## sample estimates:
## cor
## -0.8942739
The change in the logarithm of outbreak size is given by the slope parameter of this equation, i.e.
\[\begin{equation} \log10(Y) = - 0.26370x \end{equation}\]
Setting this change to one (i.e. a one log change in outbreak size), rearranging, and solving for days yields the number of days delay corresponding to a one log change in outbreak size.
\[\begin{equation} x = -3.79 \end{equation}\]
A similar analysis can be performed at the smaller spatial scale of prefectures.
It is compelling that no new prefecture has been infected since 14 February.